When Hewlett-Packard (NYSE:HPQ) CEO Meg Whitman reminisces about her early days at the helm of eBay (NASDAQ:EBAY), she fondly relates a call she got from then-SEC Chairman Arthur Levitt shortly after the blockbuster auction site went public in the fall of 1998.

Back then, EBAY stock was so volatile that it could be up 80 points and down 50 points in the same day. Then Whitman got a call from Levitt — and when the SEC called a CEO in the middle of the dot-com boom, it usually signaled concerns that manipulation was causing the stock’s volatility. But Levitt didn’t talk about eBay’s volatility. After a few pleasantries, he came to the point: As a buyer and seller of Depression glass on eBay, member feedback had just earned him a yellow star, he said, “And I thought you would just like to know.”

Whitman’s 13-year-old story illustrates one of the few enduring truths in the age of Internet, Facebook and Twitter: The buzz is as important to building brands and businesses as a company’s foundational technologies. And as a successful tech CEO who ran — and lost — an expensive race for governor of California last year, Whitman brings a lot of buzz to HPQ.

For starters, Whitman’s decision to release for free the WebOS code it acquired with its $1.2 billion purchase of Palm is crazy — like a fox. The operating system basically was wasted on HP’s TouchPad, the company’s dark horse entry into the tablet race, the last of which were liquidated on eBay over the weekend.

With her open source strategy, Whitman has the opportunity to open up a development platform potentially as feature-rich as Oracle’s (NASDAQ:ORCL) Java, drive revenue to HP’s Download Store, and potentially create a collaboration opportunity with Windows Phone.

Hewlett-Packard already is talking to Microsoft (NASDAQ:MSFT). Last week, both companies announced a four-year deal that will use HP’s cloud infrastructure to deliver Microsoft’s communications and collaboration applications to business and government customers. Both companies hope the deal will help jump-start cloud computing with customers who still have major concerns about platforms and applications that they don’t control in traditional servers and data centers.

Wall Street already has begun to receive these initiatives favorably. Since Whitman came aboard Sept. 22, HPQ shares have risen more than 20% — from below $23 to around $28. Conversely, when former SAP AG (NYSE:SAP) chief Léo Apotheker was in charge of HPQ from November 2010 to September of this year, the stock fell 46%.

But good news is fleeting, and Whitman is going to have to keep up her buzz and business strategy if she wants a long-term home at HP. Whitman is HP’s fifth CEO in six years — that’s the same number of leaders the company had in the prior 93 years. OK, two of them were interim, but an HP board that’s pining for the next William Hewlett and David Packard has been decidedly impatient with all the men and women that recently have tried to move the company into the 21st century.

Former AT&T (NYSE:T) and Lucent exec Carly Fiorina prevailed over HP’s enterprise business chief Ann Livermore in 1999 to land the top job. But a contentious marriage with Compaq helped sour the board on Fiorina, which in 2005 ousted her in an ugly scene that played out in the financial press. CFO Robert Wayman stepped in for 45 days until the board hired NCR’s Mark Hurd.

The hard-charging, cost-cutting Hurd delivered for shareholders — five years of growing revenues and stock appreciation to the tune of 130%. But Hurd resigned in 2010 after the consultant he hired — reality TV maven Jodie Fisher — accused him of sexual harassment.

Hewlett-Packard CFO Cathy Lesjak stepped in for two months until Apotheker — whom most HP board members had never met — took over in November 2010. But software-focused Apotheker’s bare-bones strategy for HP’s future, which centered on selling 100 million devices running WebOS — a plan that didn’t account for the huge head start of Apple (NASDAQ:AAPL), Nokia (NYSE:NOK) and others — sealed his fate in only 10 months.

That much recent turnover at the top — and a board whose interpersonal dynamics have compared to The Young and The Restless — clearly illustrate that HP’s biggest challenges are not limited to its products and markets. And that makes Whitman’s job a lot harder.

As of this writing, Susan J. Aluise did not hold a position in any of the aforementioned stocks.